Method and apparatus for measurement of azimuth of a borehole while drilling

This invention relates to the field of borehole measurement. More particularly, this invention relates to the field of measurement while drilling (MWD) and to a method of measuring the parameter of azimuth while the drill string is rotating.

In MWD systems, the conventional approach is to take certain borehole parameter readings or surveys only when the drillstring is not rotating. U.S. Pat. No. 4,013,945, owned by the assignee hereof, discloses and claims apparatus for detecting the absence of rotation and initiating the operation of parameter sensors for determining azimuth and inclination when the absence of rotation is sensed. While there have been several reasons for taking various MWD measurements only int he absence of drill string rotation, a principal reason for doing so is that previous methods for the measurement or determination of angles of azimuth and inclination required the tool to be stationary in order for the null points of single axis devices to be achieved; or to obtain the averaging necessary when triaxial magnetometers and triaxial accelerometers are used for determining azimuth and inclination. That is, when triaxial magnetometers and accelerometers are used, the individual field measurements necessary for determination of azimuth and inclination are dependent on instantaneous tool face angle when the measurements are taken. This is so because during rotation the x and y axis magnetometer and accelerometer readings are continually varying, and only the z axis reading is constant. In referring to x, y and z axis, the frame of reference is the borehole (and the measuring tool), with the z axis being along the axis of the borehole (and tool), and with the x and y axes being mutually perpendicular to the z axis and each other. That frame of reference is to be distinguished from the earth frame of reference to east (E), north (N) (or horizontal) and vertical (D) (or down).

There are, however, circumstances where it is particularly desirable to be able to measure azimuth and inclination while the drillstring is rotating. Examples of such circumstances include (a) wells were drilling is particularly difficult and any interruption in rotation will increase drill string sticking problems, and (b) situations where knowledge of instantaneous bit walk information is desired in order to know and predict the real time path of the borehole. A system has heretofore been proposed and used for obtaining inclination while the drillstring is rotating. In addition, U.S. patent application Ser. Nos. 054,616 and 054,552, both filed on May 27, 1987, disclose methods for obtaining azimuth measurements while rotating. Both applications are assigned to the assignee hereof, and fully incorporated herein by reference.

Unfortunately, measurement of rotating azimuth and inclination disclosed in U.S. application Ser. Nos. 054,616 and 054,552 suffer from a number of problems. The inclination (as disclosed in application Ser. No. 054,616) suffers from sensitivity problems at low inclination as well as acquisition problems due to occasional accelerometer channel saturation while drilling. Inclination while rotating is determined by gz/g using the z axis accelerometer (gz) alone and computing the arc cosine of the averaged data. The cosine response is responsible for sensitivity problems at low inclinations. The straight averaging is responsible for the error contribution of saturation. This is because except at 90° inclination, the accelerometer output is closer to saturation in one direction than the other. On average then, the accelerometer will saturate more in one direction than the other. This would have the effect of skewing the average towards zero. Equivalently, the resulting inclination error will be in the direction of 90°. This is consistent with field test data.

Similarly, the rotating azimuth measurement also is error prone. The rotating azimuth calculation requires the measurement of the magnetometer z axis (hz) output while rotating. This data is combined with total magnetic field (ht) and Dip angle measurements made while not rotating, and with inclination data. The Hz measurement is analogous to the Gz measurement for inclination except that the Hz measurement can be made quite accurately. The analogy is drawn because in the absence of tool face information, the locus of possible tool orientations knowing only inclination (from gz) is a cone around vertical. The locus of tool orientations knowing Hz, Dip angle and ht is also a cone. This cone is centered on the magnetic field axis. The rotating azimuth calculation is simply the determination of the direction of the horizontal projection of the intersection of these two cones except at 0° and 180° azimuth. This produces the east-west ambiguity in the calculation. Since the angle of intersection becomes vanishingly small as the actual azimuth approaches 0° or 180°, small errors in either cone angle measurement will result in large errors in calculated azimuth. Under some circumstances, the magnitude of this azimuth related azimuth error may be unacceptable.

The above-discussed and other problems and deficiencies of the prior art are overcome or alleviated by the method of measuring the azimuth angle of a borehole while the drill string is being rotated. In accordance with the method of the present invention, Discrete Fourier Transformations (DFT) are used to determine improved rotating azimuth and inclination measurements.

The rotating inclination measurement can be improved by determining the magnitude of the gx(t) or gy(t) signal component at the rotation frequency. Inclination can be calculation using the Gx and/or Gy magnitudes (designated as |Gx| and |Gy|) with a time averaged gz (designated as Gz)

It will be appreciated that finding the Gz or Gy spectral line corresponding to the rotation rate may be impossible without additional information. Fortunately, this information exists in the form of the hx(t) or hy(t) signal. Because these signals are not vibration sensitive, the only major spectral line in these signals will be at the rotation rate. In fact, for inclination alone, zero crossings of Hx or Hy provide sufficient information to determine rotation rate.

In accordance with the present invention, the DFT of hx(t) or hy(t) combined with the DFT of gx(t) or gy(t) and the time average of hz(t) and gz(t) provides sufficient information to determine an unambiguous azimuth. Specifically, a rotating azimuth can be accurately calculated for any orientation if inclination (Inc) (the angle between the tool axis and vertical), and magnetic inclination of theta (θ) (the angle between the tool axis and the earth's magnetic field vector), and PHI (φ) (the phase angle between the fundamental frequency component of hx(t) (or hy(t)) and that of gx(t) (or gy(t)) is known.

The above-discussed and other features and advantages of the present invention will be appreciated and understood by those of ordinary skill in the art from the following detailed description and drawings.

Referring now to the drawings, wherein like elements are numbered alike in the several FIGURES:

FIG. 1 is a block diagram of a known Computerized Direction System (CDS) used in borehole telemetry; and

FIGS. 2-13 are flow charts depicting the software used in conjunction with the method of the present invention.

The method of the present invention is intended to be implemented in conjunction with the normal commercial operation of a known MWD system and apparatus of Teleco Oilfield Services Inc. (the assignee hereof) which has been in commercial operation for several years. The known system is offered by Teleco as its CDS (Computerized Directional System) for MWD measurement; and the system includes, inter alia, a triaxial magnetometer, a triaxial accelerometer, control, sensing and processing electronics, and mud pulse telemetry apparatus, all of which are located downhole in a rotatable drill collar segment of the drill string. The known apparatus is capable of sensing the components gx, gy and gz of the total gravity field gt; the components hx, hy and hz of the total magnetic field ht; and determining the tool face angle and dip angle (the angle between the horizontal and the direction of the magnetic field). The downhole processing apparatus of the known system determines azimuth angle (A) and inclination angle (I) in a known manner from the various parameters. See e.g., the article "Hand-Held Calculator Assists in Directional Drilling Control" by J. L. Marsh, Petroleum Engineer International, July & September, 1982.

Referring to FIG. 1, a block diagram of the known CDS system of Teleco is shown. This CDS system is located downhole in the drill string in a drill collar near the drill bit. This CDS system includes a 3-axis accelerometer 10 and a 3-axis magnetometer 12. The z axis of each of the accelerometer and the magnetometer is on the axis of the drillstring. To briefly and generally describe the operation of this system, accelerometer 10 senses the gx, gy and gz components of the downhole gravity field gt and delivers analog signals commensurate therewith to a multiplexer 14. Similarly, magnetometer 12 senses the hx, hy and hz components of the downhole magnetic field ht. A temperature sensor 16 senses the downhole temperature of the accelerometer and the magnetometer and delivers a temperature compensating signal to multiplexer 14. The system also has a programmed microprocessor unit 18, system clocks 20 and a peripheral interface adapter 22. All control, calculation programs and sensor calibration data are stored in EPROM Memory 23.

Under the control of microprocessor 18, the analog signals to multiplexer 14 are multiplexed to the analog-to-digital converter 24. The output digital data words from A/D converter 24 are then routed via peripheral interface adapter 22 to microprocessor 18 where they are stored in a random access memory (RAM) 26 for the calculation operations. An arithmetic processing unit (APU) 28 provides off line high performance arithmetic and a variety of trigonometry operations to enhance the power and speed of data processing. The digital data for each of gx, gy, gz, hx, hy, hz are averaged in arithmetic processor unit 24 and the data are used to calculate azimuth and inclination angles in microprocessor 18. These angle data are then delivered via delay circuitry 30 to operate a current driver 32 which, in turn, operates a mud pulse transmitter 34, such as is described, for example, in U.S. Pat. No. 4,013,945.

In the prior art normal operation of the CDS system, the accelerometer and magnetometer readings are taken during periods of nonrotation of the drill string. As many as 2000 samples of each of gx, gy, gz, hx, hy and hz are taken for a single reading, and these samples are averages in APU 26 to provide average readings for each component. A procedure has also previously been implemented to determine inclination (I) while the drill string was rotating. In that procedure, the (Gz)1/2 component of the gravity field is determined from an average of samples obtained while rotating, and the inclination angle (I) is determined from the simple relationship ##EQU1## where Gt is taken to be 1G (i.e., the nominal value of gravity). This system is acceptable for measuring inclination while rotating, because the z axis component Gz is not altered by rotation.

In accordance with the present invention and as depicted in the flow charts of FIGS. 2-13 and Tables 2-4, the measurement of the various parameters needed to determine the tool's inclination and azimuth while rotating are as follows:

Turning first to the interrupt routine of FIGS. 2-8, throughout the measurement of the inclination and azimuth, rotation of the drill string is continuously detected by monitoring the magnetometer output hx and hy. This rotation measurement is shown in FIGS. 2 and 3 and determines the rotation direction (e.g. clockwise or counterclockwise) in addition to detecting the rate of rotation. It will be appreciated that rotation rate information of this type may be obtained by the rotation sensor for borehole telemetry disclosed in U.S. Pat. No. 4,013,945, while is assigned to the assignee hereof and fully incorporated herein by reference. It will also be appreciated that the presence of two perpendicular magnetometer sensors (hx and hy) in the CDS permits determination of direction of rotation as well.

As shown in FIGS. 4 and 5, a data sampling rate is then established such that the number of instaneous samples taken of hx, gx, hz, and gz over one tool revolution (cycle) is, on average, a constant (for example 128) from cycle to cycle. The sample rate is adjusted at the end of each cycle to maintain the constant.

Referring now to FIGS. 6 and 7, the individual samples are stored separately and two tests are conducted before the data is accepted. First, the actual number of samples taken in the last cycle is compared to the desired number and if the difference exceeds an adjustable threshold, the data is discarded. Next, the accelerometer data is scanned and if the number of samples exceeding the system's dynamic range limit is more than some predefined acceptable limit, the data is discarded.

Now referring to FIG. 8, if the data is acceptable, each point is summed into its own accumulation buffer. By summing the data from successive cycles, the data is time averaged to reduce the magnitude of non synchronous noise.

At the conclusion of the acquisition, the summed samples of hx and gx (generally called x(n)) are used to determined the discrete fourier coefficients of the fundamental (see FIG. 11) using the definition of the discrete fourier transform (DFT).

Turning now to the Main Acquisition and Calculation routine of FIGS. 9-13, the temperature corrections for the magnetometer and accelerometer sensor are calculated (FIGS. 9 and 10). Next, as shown in FIG. 11, the DFT's are determined to provide Hx, Gx, Hz and Gz. Hx, Gx, Hz and Gz are then normalized, temperatures corrected and misalignment corrected as shown in FIGS. 11 and 12.

It is generally understood that in addition to the errors due to temperature and sensor misalignment, the dynamic response of the gx and hx sensors and associated acquisition channels could introduce additional amplitude and phase errors. For gx, the errors have two potential sources: (1) The frequency response of the accelerometer and (2) the frequency response of the channel electronics.

The accelerometer used in a preferred embodiment is a type QA-1300 manufactured by Sundstrang Data Control, Inc. The frequency response of this accelerometer is flat to greater than 300 Hz. This is sufficiently above the nominal 2 to 3 Hz of tool rotation such that its effects can be neglected. The electronics channel can be designed with a frequency cut off high enough to allow its effects to be neglected as well.

The hx signal is influenced by the sensor frequency response, the electronics channel frequency response, the sensor housing frequency response and the drill collar frequency response. The electronics channel can be neglected by designing it with a high enough cut-off frequency as discussed for the accelerometer channel. Further, the magnetometer and accelerometer channels frequency response can be matched to further reduce residual phase errors.

The sensor contained in an electrically conductive housing has a frequency response which cannot be neglected. The preferred embodiment of this invention incorporates equations describing the variation of φ and |Hx| with frequency and temperature. These variations are determined by conventional calibration techniques with curve fitting techniques applied to the resulting data. The effect of the conductive drill collar is also non-negligible. Its effect can be determined by calibration. However, the preferred embodiment of this invention corrects the error by estimating the errors using the following equations: ##EQU2## where μ 0 =Free space permeability.

ω=Tool rotation rate in radians/sec.

OD=Drill collar outside diameter.

ID=Drill collar inside diameter.

R=Drill collar material resistivity in OHM-meters (usually temperature dependent).

The magnitude |Hx| is reduced by a factor A calculated as: ##EQU3##

All of the above discussed error corrections are shown in FIG. 12. Having corrected the data to compensate for error, the rotating azimuth calculation can now be performed.

Rotating azimuth (Az) can then be determined as follows: ##EQU4## where INC=angle between the tool axis and vertical (e.g. earth's gravity vector); and can be calculated as: ##EQU5## |Gx|=Magnitude of the first DFT coefficient of gx(t) sampled KN times at an adjusted rate of N samples per revolution over K tool rotations

=(Re(Gx).sup.2 +Im(Gx).sup.2).sup.1/2 (6)

Gz=Time average of gz(t) over K tool rotations ##EQU6## θ=The angle between the tool axis and the earth's magnetic field vector and can be calculated as: ##EQU7## |Hx|=Magnitude of the first DFT coefficient of hx(t) sampled N times at an adjusted rate of N samples per revolution over K tool rotations

=(Re(Hx).sup.2 +Im(Hx).sup.2).sup.1/2 (9)

Hz=Time average of hz(t) over K tool rotations ##EQU8## φ=Phase angle between the fundamental frequency component of hx(t) and that of gx(t) and can be calculated as: ##EQU9##

Equation 11 is used for clockwise rotation. Equation 11 would be multiplied by (=1) for counterclockwise rotation. ##EQU10## Tm=Period for m'th tool rotation. N=Number of samples taken in one rotation.

K=Number of tool rotations.

Equivalent equations to Equation 4 for calculating Azimuth are: ##EQU11##

In addition to Equations 4, 14, 15 and 16 and in accordance with the present invention, rotating azimuth may also be calculated using Discrete Fourier Transformations of the sample data in the following known Equation 17 (which is the equation used in calculating azimuth in the non-rotating case as discussed in the previously mentioned article by J. L. Marsh). It will be appreciated that Equations 4, 14, 15 and 16 are actually derived from Equation 17. ##EQU12## Equation 17 can be used for calculating the rotating azimuth by substituting the results of the DFT calculations for the variables in Equation 17 as set forth in Table 1:

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Perpendicular

Rotation

Sensor Used

Substitution for:

Case

Direction

Accel

MAG gx gy hx hy

__________________________________________________________________________

1 CW x x Re(Gx) -Im(Gx)

Re(Hx) -Im(Hx)

2 CW x y Re(Gx) -Im(Gx)

Im(Hy) Re(Hy)

3 CW y y Im(Gy) Re(Gy) Im(Hy) Re(Hy)

4 CW y x Im(Gy) Re(Gy) Re(Hx) -Im(Hx)

5 CCW x x Re(Gx) Im(Gx) Re(Hx) Im(Hx)

6 CCW x y Re(Gx) Im(Gx) -Im(Hy)

Re(Hy)

7 CCW y y -Im(Gy)

Re(Gy) -Im(Hy)

Re(Hy)

8 CCW y x -Im(Gy)

Re(Gy) Re(Hx) Im(Hx)

__________________________________________________________________________

Note that for Gz, use Equation 7; and for Hz use Equation 10

where Hx and Gx are defined in Equations 12-13, respectively and where Hy and Gy are defined as follows: ##EQU13##

It will be appreciated that all the information necessary to determine azimuth while rotating is contained in either the x or y sensors. The above Table 1 reflects this equivalence. It will be further appreciated that while Equations 4 and 14-16 have been discussed in terms of the x sensor, these equations are similarly valid using the y sensor and Equations 18 and 19. However, for the sake of simplicity and to avoid redundancy, the y sensor equations have not been shown.

The actual computer software which can be used to practice the above described method of calculating azimuth of a borehole while drilling is depicted in the flow charts of FIGS. 2-13. The several flow chart variables, initial state assumptions and constants are defined in TABLES 2-4 below. An example of actual source code written in Motorola 68000 assembly language for implementing the method of FIGS. 2-13 is attached hereto as a Microfiche Appendix. The flow charts of FIGS. 2-13 will be easily and fully comprehended and understood by those of ordinary skill. For ease of discussion, the flow charts of FIGS. 2-13 utilize Equation 16 to determine azimuth. However, it will be appreciated that any one of Equations 4, 14, 15 and the substituted Equation 17 may be used in the flow charts.

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Variable Description

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AccelAngle Angle of the Accelerometer `X` or `Y` axis.

Accelcosinesum

Temporary storage of the DFT calculated

cosine sum.

AccelMag Magnitude of the Accelerometer `X` or `Y`

axis.

AccelSelect

True if AccelMag and AccelAngle represent `X`

axis values. False if AccelMag and

AccelAngle represent `Y` axis values.

Accelsinesum

Temporary storage of the DFT calculated sine

sum.

AccelSummingbuffer

An array dimensioned to Samplespercycle

which contains the summed Accelerometer `X`

or `Y` axis A/D data.

AccelTempBias

A temporary variable which is an intermediate

value which converts accelerometer X or Y

axis A/D bits into temperature corrected

units of gravities.

AccelTempBuffer

An array dimensioned to Samplespercycle which

contains the Accelerometer `X` or `Y` axis

A/D data.

AccelTempScale

A temporary variable which is an intermediate

value which converts accelerometer X or Y

axis A/D bits into temperature corrected

units of gravities.

AccelZTempBias

A temporary variable which converts

accelerometer Z axis A/D bits into

temperature corrected units of gravities.

AccelZTempScale

A temporary variable which converts

accelerometer Z axis A/D bits into

temperature corrected units of gravities.

AccelZ Magnitude of the Accelerometer `Z` axis.

AcceptClip The acceptable number of Samplespercycle data

sets that can experience clipping and still

be acceptable for inclusion of this rotation

in the final analysis.

Accounts The number of executions of the interrupt

routine during this revolution of the

downhole tool.

Acqcycles Number of tool revolutions over which the raw

Magnetometer and Accelerometer data was

acquired.

AcquireData

Executes the interrupt routine when True

(Performs rotating data acquisition).

Bypasses the interupt routine when False.

AcquisitionDuration

The amount of time over which the rotating

azimuth and inclination raw data is acquired.

Anmisperslice

The ratio of the actual number of interupt

routine executions per revolution to the

desired number used in the Astate machine.

Astate One of two state machines in the interupt

routine which acquires the data that is later

used for the calculation of rotating azimuth

and inclination.

Atemp Loop index used in the Astate machine.

Azimuth 0 to 360 degrees from magnetic north.

DrillpipeID

Inside diameter of the drill pipe of the

downhole tool.

DrillpipeOD

Outside diameter of the drill pipe of the

downhole tool.

EPSILON3 Variable which contains the phase error

corrections associated with rotation.

EPSILON4 Variable which contains the magnitude

corrections associated with rotation.

GMAX The A/D raw reading which if a raw

accelerometer reading is equal or greater

than constitutes clipping.

GMIN The A/D raw reading which if a raw

accelerometer reading is equal of less than

constitutes clipping.

Ground Magnitude of the ground signal in the same

scaling as AccelZ and magZ.

GX Temporary variable used to store either

TempGx or TempGy based upon AccelSelect.

Gxclip The number of Samplespercycle data sets that

have experience clipping on the X or Y

accelerometer axis. Whichever is specified

by AccelSelect.

Gzclip The number of Samplespercycle data sets that

have experience clipping on the Z

accelerometer axis.

HX Temporary variable used to store either TemHx

or TempHy based upon MagSelect.

Inclination

0 to 90 degrees from line which points to

center of the earth.

Index Loop counter temporary variable.

KA0-KA3 Temporary variables used to represent

KGXA0-KGXA3, KGYA0-KGYA3, KHXA0-KHXA3,

KHYA0-KHYA3 to reduce the number of equations

that have to be coded.

KB0-KB3 Temporary variables used to represent

KGXB0-KGXB3, KGYA0-KGYA3, KHYA0-KHYA3 to

reduce the number of equations that have to

be coded.

KGSCLF Constant used to scale accelerometer A/D bits

into units of gravities.

KGXA0-KGXA3

Constants used to temperature correct the

accelerometer X axis.

KGXB0-KGXB3

Constants used to temperature correct the

accelerometer X axis.

KGYA0-KGYA3

Constants used to temperature correct the

accelerometer Y axis.

KGYB0-KGYB3

Constants used to temperature correct the

accelerometer Y axis.

KGZA0-KGZA3

Constants used to temperature correct the

accelerometer Z axis.

KGZB0-KGZB3

Constants used to temperature correct the

accelerometer Z axis.

KHSCLF Constant used to scale magnitometer A/D bits

into units of gauss.

KHXA0-KHXA3

Constants used to temperature correct the

magnetometer X axis.

KHXB0-KHXB3

Constants used to temperature correct the

magnetometer X axis.

KHYA0-KHYA3

Constants used to temperature correct the

magnetometer Y axis.

KHYB0-KHYB3

Constants used to temperature correct the

magnetometer Y axis.

KHZA0-KHZA3

Constants used to temperature correct the

magnetometer Z axis.

KHZB0-KHZB3

Constants used to temperature correct the

magnetometer Z axis.

K1A0-K1A3 Constants used to temperature correct the

constant K1EPSILON3

K1EPSILON3 Constant used to frequency correct the

variable EPSILON3.

K1EPSILON4 Constant used to frequency correct the

variable EPSILON4.

K1Temp Constant used to convert the raw A/D input

for temperature into degrees centigrade.

K2A0-K2A3 Constants used to temperature correct the

constant K2EPSILON3

K2EPSILON3 Constant used to frequency correct the

variable EPSILON3.

K2EPSILON4 Constant used to frequency correct the

variable EPSILON4.

K2Temp Constant used to convert the raw A/D input

for temperature into degrees centigrade.

K3A0-K3A3 Constant used to frequency correct the

constant K3EPSILON3

K3EPSILON3 Constant used to frequency correct the

variable EPSILON3.

K3EPSILON4 Constant used to frequency correct the

variable EPSILON4.

Last.sub.-- Quadrant

Value of Quadrant during the last execution

of the interrupt routine.

MagAngle Angle of the Accelerometer `X` or `Y`.

Magcosinesum

Temporary storage of the DFT calculated

cosine sum.

MagMag Magnitude of the Magnetometer `X` or `Y` axis.

MagSelect True if MagMag and MagAngle represent the `X`

axis. False if MagMag and MagAngle represent

the `Y` axis.

Magsinesum Temporary storage of the DFT calculated sine

sum.

MagSumminbuffer

An array dimensioned to Samplespercycle which

contains the Magnetometer `X` or `Y` axis A/D

data.

MagTempBias

A temporary variable which is an intermediate

value which converts magnetometer X or Y axis

A/D into temperature corrected units of gauss.

MagTempbuffer

An array dimensioned to Samplespercycle which

contains the Magnetometer `X` or `Y` axis A/D

data.

MagTempScale

A temporary variable which is an intermediate

value which converts magnetometer X or Y axis

A/D into temperature corrected units of gauss.

MagZTempBias

A temporary variable which converts

magnetometer Z axis A/D bits into temperature

corrected units of gauss.

MagZTempScale

A temporary variable which converts

magnetometer Z axis A/D bits into temperature

corrected units of gauss.

MAGZ Magnitude of Magnetometer `Z` axis.

MTF Magnetic Tool Face is the angle between the

magnetometer and accelerometer angles.

Pi 3.14159 . . . etc.

RawTemp Acutal A/D reading for temperature.

Rcounts The number of interrupt routine executions in

a complete revolution of the downhole tool.

Rotation.sub.-- Clock

A value between 0 and 12 seconds. It is the

interval over which a check is made if the

tool is rotating.

Rotation.sub.-- Detection

The number of consecutive quadrants that the

tool has rotated in the same direction. If

positive then the direction was clockwise.

If negative then the direction was

counterclockwise.

Rotation.sub.-- Detection

If the tool is rotating then this variable is

either CW for clockwise or CCW for

counterclockwise.

Rotation.sub.-- Setpoint

The number of consecutive quadrant changes

in the same rotation direction that

constitute the declaration that the tool is

rotating.

Rotating True if the tool is rotating about its Z

axis. False if it is not rotating about its

Z axis.

Rnmispercyle

The number of interrupt routine executions in

a complete revolution of the downhole tool.

Rnmisperslice

The ratio of the actual number of interput

routine executions per revolution to the

desired number.

RHO0 Constant.

Rstate One of two state machines in the interupt

routine which determines the length of the

rotation period of the downhole tool.

Samplespercycle

Number of identical intervals each tool

revolution is divided into. Raw

Accelerometer and Magnetometer data is

acquired at each interval.

Temperature

Temperature of the downhole tool in degrees

centigrade.

TempValid True if the value of the variable Temperature

is valid. False if the value of the variable

Temperature in invalid.

Trigger Value indicates to take one of the

Samplespercycle data sets.

__________________________________________________________________________

______________________________________

Variable Value

______________________________________

AcquireData False

AcquisitionDuration

20 Seconds.

DrillPipeID Diameter of the inside of the drill collar

that the downhole tool mounts inside of.

DrillPipeOD Diameter of the outside of the drill collar

that the downhole tool mounts inside of.

TempValid False.

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TABLE 4

Constants Which are Determined by Calibration Procedures KGSCLF, KHSCLF, KGXA0-KGXA3, KGXBO-KGXB3, KGYAO-KGYA3, KGYBO-KGYB3, KGZA0-KGZA3, KGZBO-KGZB3, KHXA0-KHXA3, KHXB0-KHXB3, KHYAO-KHYA3, KHYBO-KHYB3, KHZA0-KHZA3, KHZB0-KHZB3, K1A0-K1A3, K2A0-K2-A3, K3A0-K3A3, K1Tempm K2Temp

While preferred embodiments have been shown and described, various modifications and substitutions may be made thereto without departing from the spirit and scope of the invention. Accordingly, it is to be understood that the present invention has been described by way of illustrations and not limitation.